QCD is the fundamental theory which describes the dynamics of quarks and gluons. If we understand the dynamics at finite density and temperature, i.e. QCD phase diagram and equation of states, we can progress many studies such as the studies of unstable nucleus, nuclear fusion, early universe and neutron stars. The study of QCD phase diagram is very interesting, but we have not understood it well for a long time. This is because we face a problem in this thesis at finite density. The problem is called the sign problem. It causes a decrease of the calculation accuracy. That is why we can not calculate physical quantities with high accuracy at finite chemical potential.In this thesis, we try to beat the sign problem using the canonical approach of finite density lattice QCD. Although it is known that the canonical approach has several numerical problems, we can reduce them and calculate thermodynamic observables well at finite density. Concretely, in order to reduce the computation cost of the fermion determinant, we use the winding number expansion, in order to enhance the calculation accuracy of physical quantities, we adopt the multi precision calculation to our program based on the canonical approach. In this thesis, we will see how to improve the canonical approach and a result of thermodynamic observables which is related with the QCD phase transition at finite density.Our result shows that we do not observe the peak which represents the confinementdeconfinement phase transition in baryon number susceptibility. Therefore, we do not see the QCD phase transition yet. However, in this thesis, we find that canonical approach can explore the QCD phase diagram beyond µ B /T = 3 (µ B is the baryon chemical potential). That is, we explored the QCD phase structure beyond the validity range of Taylor expansion and reweighting method. This opens a bright window of study of QCD phase diagram at finite density. With our improvement, canonical approach has the possibility for investigation of thermodynamic observables at any chemical potential.